Solve x^2=384

$${ x }^{ 2 } =384$$

Solve for x

$$x=8\sqrt{6}\approx 19.595917942$$

$$x=-8\sqrt{6}\approx -19.595917942$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=8\sqrt{6} x=-8\sqrt{6}$$

Steps Using the Quadratic Formula

Subtract 384 from both sides.

$$x^{2}-384=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -384 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-384\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-384\right)}}{2}$$

Multiply -4 times -384.

$$x=\frac{0±\sqrt{1536}}{2}$$

Take the square root of 1536.

$$x=\frac{0±16\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{6}}{2} when ± is plus.

$$x=8\sqrt{6}$$

Now solve the equation x=\frac{0±16\sqrt{6}}{2} when ± is minus.

$$x=-8\sqrt{6}$$

The equation is now solved.

$$x=8\sqrt{6} x=-8\sqrt{6}$$